A ball mass 500g rolls at a velocity of 2m/s and hits another ball of mass 250g

1.What is the velocity of a small ball if the bigger ball immediately stops after collision?
2.What is the velocity of the bigger ball if it rolls in the same direction with the smaller ball at 0.5m/s?

You can answer both questions using conservation of momemtum. You do not have to assume an elastic collision. In fact, neither collision is elastic.

Let the masses of the two balls be M (500 g) and m (250 g). Let Vo be the initial velocity of M.

Let V be the final velocity of the big ball.
Let v be the final velocity of the small ball

1. M*Vo = m*v
v = (M/m)*Vo = 4 m/s

2. M*(2 m/s) = (0.5 m/s)*M + m*v
M*(1.5 m/s) = m*v
v = (M/m)*(1.5 m/s) = 3.0 m/s

To answer these questions, we can apply the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces are acting on the system.

1. To find the velocity of the smaller ball after the collision, we can consider the collision as an isolated system where the two balls interact. The momentum before the collision is given by the formula:

Initial momentum = (Mass of ball 1 * Velocity of ball 1) + (Mass of ball 2 * Velocity of ball 2)

Since the bigger ball immediately stops after the collision, its velocity will be zero. Thus, the initial momentum becomes:

Initial momentum = (Mass of ball 1 * Velocity of ball 1)

Substituting the values, we have:

Initial momentum = (0.5 kg * 2 m/s) = 1 kg⋅m/s

Since momentum is conserved, the final momentum will also be 1 kg⋅m/s. Let's assume the final velocity of the smaller ball is v.

Final momentum = (Mass of ball 1 * Velocity of ball 1) + (Mass of ball 2 * Velocity of ball 2)

Final momentum = (0.25 kg * v) + (0 kg * 0)

Since the bigger ball has zero velocity after the collision, its term becomes zero. Substituting the values, we have:

1 kg⋅m/s = (0.25 kg * v)
v = (1 kg⋅m/s) / (0.25 kg)
v = 4 m/s

Therefore, the velocity of the smaller ball after the collision is 4 m/s.

2. To find the velocity of the bigger ball if it rolls in the same direction with the smaller ball at 0.5 m/s, we again consider the collision as an isolated system.

Using the principle of conservation of momentum, we have:

Initial momentum = (Mass of ball 1 * Velocity of ball 1) + (Mass of ball 2 * Velocity of ball 2)

Let's assume the final velocity of the bigger ball is V.

Final momentum = (Mass of ball 1 * Velocity of ball 1) + (Mass of ball 2 * Velocity of ball 2)

Substituting the values, we have:

Initial momentum = (0.5 kg * 0 m/s) + (0.25 kg * 0.5 m/s)
Initial momentum = 0 kg⋅m/s

Final momentum = (0.5 kg * V) + (0.25 kg * 0.5 m/s)

Since momentum is conserved, the initial and final momenta are equal:

0 kg⋅m/s = (0.5 kg * V) + (0.25 kg * 0.5 m/s)

0 = 0.5V + 0.125
0.5V = -0.125
V = -0.25 m/s

Therefore, the velocity of the bigger ball after the collision, in the same direction as the smaller ball, is -0.25 m/s. The negative sign indicates that the direction of the ball is opposite to the initial direction.